Soldier Boy is seen pouring Coca Cola into a glass of milk and drinking the mixture. This is a hangover cure from 1938.
Homelander tells Black Noir that unlike others, he can clearly see his face due to his ability of X-ray vision. This is a subtle dig at a plot loophole in the comics. While Black Noir's identity is a crucial part of the comics' plot, Homelander never once attempts to see past Black Noir's cloth mask.
The irresistible urge to pull your hair out is a mental disorder called Trichotillomania.
The names of the runners in the track meet that Nathan is watching on TV are the names of the crew members from the post-production and VFX departments.
Soldier Boy makes an extremely crude joke about an encounter with Jane Wyman at the 24th Academy Awards held in 1952 (where An American in Paris (1951) won Best Picture, as he mentions). The subject matter of this joke also shows how much Soldier Boy's mind is still stuck the 1980s (when he was captured) since this joke would have been even more tasteless and shocking if told at that time when it was much more commonly known that Jane Wyman was the first wife of Ronald Reagan - the president of the US, at the time.